t(44-3t)=105

Solution for t(44-3t)=105 equation:

Simplifying
t(44 + -3t) = 105
(44 * t + -3t * t) = 105
(44t + -3t2) = 105

Solving
44t + -3t2 = 105

Solving for variable 't'.

Reorder the terms:
-105 + 44t + -3t2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + 44t + -3t2 = 0

Factor a trinomial.
(-35 + 3t)(3 + -1t) = 0

Subproblem 1
Set the factor '(-35 + 3t)' equal to zero and attempt to solve:

Simplifying
-35 + 3t = 0

Solving
-35 + 3t = 0

Move all terms containing t to the left, all other terms to the right.

Add '35' to each side of the equation.
-35 + 35 + 3t = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 3t = 0 + 35
3t = 0 + 35

Combine like terms: 0 + 35 = 35
3t = 35

Divide each side by '3'.
t = 11.66666667

Simplifying
t = 11.66666667
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {11.66666667, 3}